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Directors:
Randolph E. Bank
Philip E. Gill
Michael Holst

Juan Rodriguez

Office: AP&M 7409
Phone: (858)534-9056
Fax: (858)534-5273
E-mail: jcr009@ucsd.edu
On the Continuity of Exterior Differentiation Between Sobolev-Slobodeckij Spaces of Sections of Tensor Bundles on Compact Manifolds

UCSD

Abstract:

Suppose Ω is a nonempty open set with Lipschitz continuous boundary in \mathbbRn. There are certain exponents e ∈ R and q ∈ (1,∞) for which [(∂)/(∂xj)]: We,q(Ω)→ We−1,q(Ω) is NOT a well-defined continuous operator. Now suppose M is a compact smooth manifold. In this talk we will try to discuss the following questions:

1. How are Sobolev spaces of sections of vector bundles on M defined?

2. Is it possible to extend d: C(M)→ C(T*M) to a continuous linear map from We,q(M) to We−1,q(T*M) for all e ∈ R and q ∈ (1,∞)?

3. Why are we interested in the above question?

Tuesday, May 9, 2017
11:00AM AP&M 2402